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High Dimensions and Heavy Tails for Natural Evolution Strategies (2011)
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| Venue: | In Genetic and Evolutionary Computation Conference (GECCO |
| Citations: | 13 - 10 self |
BibTeX
@INPROCEEDINGS{Schaul11highdimensions,
author = {Tom Schaul and Tobias Glasmachers and Jürgen Schmidhuber},
title = {High Dimensions and Heavy Tails for Natural Evolution Strategies},
booktitle = {In Genetic and Evolutionary Computation Conference (GECCO},
year = {2011}
}
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Abstract
The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness on the parameters of its search distribution. While general in its formulation, existing research has focused only on multivariate Gaussian search distributions. We address this shortcoming by exhibiting problem classes for which other search distributions are more appropriate, and then derive the corresponding NES-variants. First, we show how simplifying NES to separable distributions reduces its complexity from O(d 3) to O(d), and apply it to problems of previously unattainable dimensionality, recovering lowest-energy structures on the Lennard-Jones atom clusters and state-of-the-art results on neuro-evolution benchmarks. Second, we develop a new, equivalent formulation based on invariances, which allows us to generalize NES to heavy-tailed distributions, even if their variance is undefined. We theninvestigate howthisvariant aids inovercoming deceptive local optima.
Keyphrases
natural evolution strategy heavy tail high dimension search distribution simplifying ne multivariate gaussian search distribution howthisvariant aid equivalent formulation principled approach natural gradient expected fitness lennard-jones atom cluster lowest-energy structure unattainable dimensionality real-valued evolutionary optimization problem class deceptive local optimum state-of-the-art result corresponding nes-variants neuro-evolution benchmark heavy-tailed distribution
